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Solve Differential Equations using Laplace Transformation
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  • Course
  • Differential Equations
  • Institution
  • Khwaja Fareed University Of Engineering And Information Technology

In this documents, there are important formulas of Laplace that help you to solve differential equation of Mathematics and also AC Network equations. In this documents there is only formulas of Laplace.

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Document information

  • July 8, 2021
  • 1
  • 2020/2021
  • Class notes
  • Engr. muhammad umer
  • All classes

Subjects

  • differential equations
  • laplace transformation
  • laplace

Written for

  • Khwaja Fareed University of Engineering and Information Technology
  • Differential Equations
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Laplace Transformation Formulas
1
1. L[1] =
𝑠
𝑛!
2. L[t] =
𝑠^𝑛+1
1
3. L[eαt] =
𝑠−𝛼
-αt 1
4. L[e ] =
𝑠+𝛼
𝛽
5. L[sinβt] =
𝑠^2+ 𝛽^2
𝑠
6. L[cosβt] =
𝑠^2+ 𝛽^2



Laplace Differential equation Transformation
1. L[Dx] = sx(t) – x(0)
2. L[D2x] = s2x(t) – sx(0) – x’(0)
3. L[D3x] = s3x(t) – s2x(0) – sx’(0) – x’’(0)
4. L[D4x] = s4x(t) – s4x(0) – s2x’(0) – sx’’(0) – x’’’(0)
5. L[D5x] = s5x(t) – s4x(0) – s3x’(0) – s2x’’(0) – sx’’’(0) – x’’’’(0)

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